有限时间水平线,半线上的阻止者与奇异控制者博弈

Andrea Bovo, Tiziano De Angelis
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引用次数: 0

摘要

我们证明了在有限时间视界上双人零和阻止者与奇异控制者博弈值的存在性,当底层动力学是一维的、扩散性的并注定在 $[0,\infty)$ 中演化时。我们证明,在 $[0,T)\times\{0\}$ 时,该值是一个变分不等式的最大解,同时具有障碍和梯度约束,并满足迪里希特边界条件。与现有的相关文献相比,我们引入了新的概率方法,以获得近似变分不等式的受罚偏微分方程(PDE)解的梯度边界和等连续性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Finite-time horizon, stopper vs. singular-controller games on the half-line
We prove existence of a value for two-player zero-sum stopper vs. singular-controller games on finite-time horizon, when the underlying dynamics is one-dimensional, diffusive and bound to evolve in $[0,\infty)$. We show that the value is the maximal solution of a variational inequality with both obstacle and gradient constraint and satisfying a Dirichlet boundary condition at $[0,T)\times\{0\}$. Moreover, we obtain an optimal strategy for the stopper. Compared to the existing literature on this topic, we introduce new probabilistic methods to obtain gradient bounds and equi-continuity for the solutions of penalised partial differential equations (PDE) that approximate the variational inequality.
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